#### Date of Graduation

5-2018

#### Document Type

Dissertation

#### Degree Name

Doctor of Philosophy in Physics (PhD)

#### Degree Level

Graduate

#### Department

Physics

#### Advisor

Surendra Singh

#### Committee Member

Reeta Vyas

#### Second Committee Member

Min Xiao

#### Third Committee Member

Salvador Barraza-Lopez

#### Fourth Committee Member

Brajendra Panda

#### Keywords

Beam, Diffraction, Gaussian, Laguerre, Laser, Vortex

#### Abstract

The natural phenomenon of waves bending around obstacles is diffraction. Spatial characteristics of the diffraction pattern depends on the incident wave field, the shape, and size of the aperture. The diffraction of a plane wave of light by a slit and a circular aperture produce the sinc-squared and the Airy intensity patterns, respectively. On the contrary, the diffraction of Laguerre-Gauss vortex (LGV) beams by simple apertures such as a slit, circular apertures, and polygons show many unexpected features.

LGV beams have $\rho^{\ell}e^{i\ell\phi}$ transverse spatial dependence, where $\rho$ is the distance from the beam axis, $\phi$ the azimuthal angle, and $\ell$ is the index of orbital angular momentum that corresponds to $\ell\hbar$ of orbital angular momentum per photon. The LGV beams were produced from Hermite-Gauss beams using an astigmatic mode converter. The LGV beams were diffracted by a slit, circular apertures, and polygons. The far-field diffraction pattern was recorded.

LGV beam of order $\ell$ when diffracted by a slit at the beam waist showed, $\ell+1$ fringes. The diffraction performed along the direction of propagation, away from the waist, showed a shear in the pattern, with maximum shear at Rayleigh range. As the slit was moved even further away, the diffraction pattern evolved into two dominant peaks irrespective of $\ell$. When LGV beams of order $\ell$ are diffracted by a circular aperture, the minima of the diffracted field depend on the zeros of $\ell+1$ order Bessel functions. The center of the diffraction pattern has a minimum for $\ell\geq 1$. When the beam axis and the aperture axis are laterally separated, this central minimum splits into $\ell$ minima. The diffraction of LGV beams by regular polygons created an optical lattice. The diffraction pattern by a regular polygon of $n$ sides has $n-$fold symmetry for both even and odd $n$, unlike the $2n-$fold symmetry for odd $n$, and $n-$fold for even $n$ due to a plane wave. The center of the diffraction pattern is bright for $\ell=n$, and multiples of $n$. The diffraction pattern has a repeating, nesting structure for $\ell>n$. The experimental results are in good agreement with the theoretical predictions.

#### Recommended Citation

Ambuj, Anindya, "Diffraction of Laguerre Gaussian Vortex Beams" (2018). *Theses and Dissertations*. 2761.

https://scholarworks.uark.edu/etd/2761